Graded Lattice Structures Research Articles

Multi-scale and multi-material topology optimization of gradient lattice structures using surrogate models

Lattice structures have received considerable attention in the recent years due to the increasingly high flexibility and resolution offered by additive manufacturing techniques. They also present an attractive design approach for applications such as aerospace and biomedical engineering due to their desirable properties including lightweight, high specific strength and stiffness and heat dissipation. This work explores a computationally efficient topology optimization approach while increasing the flexibility of a restricted unit cell design. Unrestricted material unit cell designs are often associated with high computational power and connectivity problems, while highly restricted lattice unit cell designs may lack the potential to reach the optimal desired properties at a reduced computational effort. A two-scale concurrent optimization of lattice structure is proposed in this study, where the topology optimization at the macro-scale structure and the underlying material micro-structures is performed simultaneously to achieve optimal topologies. Surrogate models are used to represent material and geometrical properties for a continuous topology optimization approach. An energy-based homogenization method combined with voxelization is employed to obtain the elasticity tensors for a lattice unit cell library. A multi-variable parameterization of the material unit cell is defined, which allows for the synthesis of functionally graded lattice structures. A multi-material extension to the concurrent multi-scale topology optimization is also explored. The performance of the optimized graded lattice structure is compared to a uniform lattice structure.

Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method

Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method

Numerical Investigation of Ti6Al4V Gradient Lattice Structures with Tailored Mechanical Response

Open porous lattice structures have found a wide range of applications as lightweight load‐bearing and energy absorbent structures in various fields. A common requirement for any application is the preliminary assessment of the mechanical response of the proposed architecture. Herein, uniform and continuous functionally graded lattice structures (FGLSs) made of titanium alloy, Ti–6Al–4V, are designed using cubic and pillar octahedron unit cells at overall porosities of 60%, 75%, and 85%. The lattice morphology is modulated using axial, dense‐in, and dense‐out gradient strategies. The mechanical performance of the structures is studied using numerical simulations implementing damage initiation and evolution under quasi‐static compression. The proposed models could properly simulate the mechanical properties and failure behavior of the lattice structures. The designed FGLSs displays a crushing behavior starting from the lower relative density layers toward the higher relative density ones. Cubic and pillar octahedron‐based structures exhibit stretch‐ and bending‐dominated deformation behaviors, respectively. The power‐law analysis verified by the Gibson–Ashby model is used to assess the mechanical response of the FGLSs. The effect of the gradient strategies on the mechanical properties as well as their adaptability for orthopedic implants is discussed in detail.

Design and mechanical performances of a novel functionally graded sheet-based lattice structure

Functionally graded lattice structures have been promoted as the next-generation multifunctional material with unique physical and mechanical performances. In this study, a parametric design approach was proposed for the design of a novel functionally graded sheet-based BCC (FGSB) lattice structure. The lattice model was defined by a single closed shell with triangular facets which can be directly used to generate the STL file for additive manufacturing. Using this design approach, the FGSB lattice structures with varying gradient directions were designed and fabricated by laser powder bed fusion (LPBF). The deformation behavior, mechanical properties, and energy absorption behavior of the FGSB lattice structures were investigated. The results show that the FGSB lattice structures with the gradient perpendicular to the load direction eliminated the randomness of shear failure and exhibited the highest elastic modulus, yield strength, and compression strength. The FGSB lattice structures with the gradient parallel to the load direction absorbed the largest amount of energy up to densification point due to the distinct layer-by-layer deformation behaviors and the gradually enhanced energy absorption capability. Moreover, the deformation behavior of lattice structures was successfully simulated by the finite element method. Finally, with this design approach, a pillow bracket infilled with large-scale FGSB lattice structures was designed according to the boundary geometry and topology optimization results, demonstrating the effectiveness of the proposed design approach for lightweight applications.

Mechanical responses of sheet-based gyroid-type triply periodic minimal surface lattice structures fabricated using selective laser melting

Owing to their lightweight design, high energy absorption capacity, and excellent thermal and sound insulation properties, lattice structures have many potential applications in the fields of security, aerospace, biomedicine, and heat dissipation. In this study, a gyroid-type triply periodic minimal surface is used to design lattice structures. Gyroid uniform lattice structures and gyroid graded lattice structures are mathematically designed and fabricated using selective laser melting with a SS 316 L stainless steel powder. The mechanical properties of these structures are studied under a compression load, and the deformation differences between the graded and uniform structures are compared. The finite element method is used to simulate the compression process, and the experimental and simulation results are qualitatively compared. Results show that during plastic deformation, the stress change in the graded structure is larger than that in the uniform structure. By controlling the volume fraction, mechanical properties can be specifically tailored, which provides the design guidelines for the application of this structure.

Compressive Properties of Ti6al4v Functional Graded Lattice Structures Via Topology Optimization Design and Selective Laser Melting Fabrication

Compressive Properties of Ti6al4v Functional Graded Lattice Structures Via Topology Optimization Design and Selective Laser Melting Fabrication

Effect of Lattice Structure and Composite Precursor on Mechanical Properties of 3D-Printed Bone Scaffolds

This article presents an investigation on designing and fabricating scaffolds with different structures, desired porosity, composition, and surface area to volume ratio (SA:V) for orthopedic applications by using the computer-aided design (CAD) and the stereolithography (SLA) 3D printing technique. Different triply periodic minimal surfaces (TPMS) and functionally graded lattice structures (FGLS) were designed based on various cell geometries. Finite element analysis (FEA), tensile and compression tests were carried out, and the results are presented. Two different resin compositions were used to print the models and compare the effect of resin precursors on the mechanical properties of scaffolds. The first was a biodegradable resin made from soybean oil commercially available on the market (made by Anycubic Co.). The second was a mixture of biodegradable UV-cured resin with 5% W/W of hydroxyapatite (HA) and 5% W/W calcium pyrophosphate (CPP). Bio-Hydroxyapatite and Bio-Calcium Pyrophosphate were obtained from eggshells waste and characterized using XRD and FESEM. The obtained data show that adding resin precursors (HA/CPP) slightly decreases the mechanical strength of printed scaffolds; however, considering their extraordinary effect on bone regeneration, this small effect can be ignored, and HA/CPP can be used as an ideal agent in bioscaffolds.

Influence of relative density distribution rules on the mechanical compression responses of additive manufactured Ti6Al4V graded lattice structures

To reveal the mapping mechanism between relative density distribution rules and compression responses of Graded lattice structures (GLSs), this work formed a series of lattice structures by establishing a theoretical model and adjusting distribution functions. To quantitatively describe the gradient variation rule, the degree of gradient (Dg ) was introduced. Combined with quasi-static compression experiment and numerical simulation, compression responses of lattice structures were analyzed. The results demonstrated that relative density distribution rules could adjust the compression responses and achieved the transformation of the failure mode, and Dg was negatively related to the mechanical properties and the energy absorption capacity. Therefore, using relative density distribution rules can predict the overall performance and provide a reference for the novel graded lattice structural design.

The Effect of Functional Gradient Material Distribution and Patterning on Torsional Properties of Lattice Structures Manufactured Using MultiJet Fusion Technology.

Functionally graded lattice structures have attracted much attention in engineering due to their excellent mechanical performance resulting from their optimized and application-specific properties. These structures are inspired by nature and are important for a lightweight yet efficient and optimal functionality. They have enhanced mechanical properties over the uniform density counterparts because of their graded design, making them preferable for many applications. Several studies were carried out to investigate the mechanical properties of graded density lattice structures subjected to different types of loadings mainly related to tensile, compression, and fatigue responses. In applications related to biomedical, automotive, and aerospace sectors, dynamic bending and rotational stresses are critical load components. Therefore, the study of torsional properties of functionally gradient lattice structures will contribute to a better implementation of lattice structures in several sectors. In this study, several functionally gradient triply periodic minimal surfaces structures and strut-based lattice structures were designed in cylindrical shapes having 40% relative density. The HP Multi Jet Fusion 4200 3D printer was used to fabricate all specimens for the experimental study. A torsional experiment until the failure of each structure was conducted to investigate properties of the lattice structures such as torsional stiffness, energy absorption, and failure characteristics. The results showed that the stiffness and energy absorption of structures can be improved by an effective material distribution that corresponds to the stress concentration due to torsional load. The TPMS based functionally gradient design showed a 35% increase in torsional stiffness and 15% increase in the ultimate shear strength compared to their uniform counterparts. In addition, results also revealed that an effective material distribution affects the failure mechanism of the lattice structures and delays the plastic deformation, increasing their resistance to torsional loads.

The influence of geometric defects and microstructure in the simulation of the mechanical behaviour of laser powder-bed fusion components: Application to endoprosthesis

This work aims at enabling the fabrication of a new generation of prosthetic components with enhanced mechanical behaviour and an extended lifetime. Cobalt‑chromium lattice structures manufactured using laser powder bed fusion are analysed to quantify the influence of microstructural anisotropy and geometrical deviations on stiffness prediction. Results of the experimental campaign are used to improve finite-element modelling of the mechanical behaviour of functionally graded lattice structures. The proposed method, which can be extended to any lattice structure fabricated by laser powder bed fusion, is then used to redesign an ankle prosthetic component.

Fatigue properties of Ti-6Al-4V Gyroid graded lattice structures fabricated by laser powder bed fusion with lateral loading

Graded lattice structures (GLSs) have drawn much attention in engineering and biological areas due to the enhanced mechanical properties and energy absorption capacity that benefit from the graded design. This study aims to investigate the effect of gradient on fatigue behaviors of lattice structures under the cyclic loading lateral to the gradient direction. The Gyroid-type triply periodic minimal surface was utilized to design GLS with continuously varied volume fraction (VF) from 10% to 40%. Uniaxial compressive testing and compression-compression fatigue testing were conducted on the Ti-6Al-4V Gyroid lattice structures with both uniform and graded VFs fabricated by laser powder bed fusion. Three typical fracture modes and mixed fracture modes were all observed on the fracture surfaces of struts after fatigue testing. The fatigue life of Gyroid GLSs is 1.21–1.67 times that of uniform counterparts with an identical overall VF. The enhancement mechanism on fatigue properties coming from the gradient design is elaborated through the finite element analysis and experimental characterization. The lower level of tensile stress, bigger macro-area and micro-plastic zone on struts of the main loading-bearing constituent of Gyroid GLS relieve the stress concentration around the crack tip, thus, lower the crack propagation rate and provide stronger fatigue crack resistance. Furthermore, the struts in the main loading-bearing constituent are more prone to stretching, therefore, provide long-term carrying capacity even after the occurrence of penetrating cracks. Experiment results show that the carrying capacity can be still provided by these struts even with penetrating cracks. • Gyroid graded lattice structures were designed and made via laser powder bed fusion. • Three basic fracture modes and mixed modes were observed from the fracture surfaces. • Thick struts in the graded lattice structure has a lower tensile stress. • Few penetrating cracks do not lower the carrying capacity of the graded lattice. • The gradient design dramatically improves the fatigue properties.

Fatigue behaviour and biocompatibility of additively manufactured bioactive tantalum graded lattice structures for load-bearing orthopaedic applications

Laser powder bed fusion (LPBF) additive manufacturing of pure tantalum and their graded lattice structures was systematically investigated, with emphasis on their microstructure evolution, phase formation, surface energy and biological properties in comparison with conventionally forged pure Ta. The LPBF fabricated Ta (LPBF-Ta) exhibited lower contact angles and higher surface energy than the forged-Ta which indicated the better wettability of the LPBF-Ta. The adhesion and proliferation of rat bone marrow stromal cells (rBMSCs) were also enhanced for the LPBF-Ta when compared to forged-Ta. Three different Ta graded gyroid lattice structures (i.e., uniform structure, Y-gradient structure, Z-gradient structure) were designed and fabricated using the same optimised LPBF parameters. Y-gradient structures exhibited the best plateau stress and compressive modulus among three different graded structures due to the maximum local volume fraction on the fracture plane. In fatigue response, Y-gradient outperformed the other two gyroid structures under varying stresses. In terms of cell culture response, the uniform structures performed the best biocompatibility due to its suitable pore size for cell adhesion and growth. This study provides new and in-depth insights into the LPBF additive manufacturing of pure Ta graded lattice structures with desired fatigue and biological properties for load-bearing orthopaedic applications.

Quasi-Static compressive responses and fatigue behaviour of Ti-6Al-4 V graded lattice structures fabricated by laser powder bed fusion

Graded lattice structures have been paid wide attention in the engineering and biological fields due to their excellent energy absorption capacity and variable porosity characteristics. Based on the size-graded lattice structure, laser powder bed fusion is utilized to manufacture the corresponding Ti-6Al-4 V lattice samples. Then, the quasi-static compression experiment is conducted and a predictive model for its mechanical properties is established accordingly. Also, its dynamic fatigue behavior is studied, and the influence of sandblasting and gradient direction on its mechanical response is evaluated. The results show that excellent mechanical properties and energy absorption capacity is exhibited in the vertical graded (VG) structure. Compared to the uniform structure, its elastic modulus and energy absorption are increased by 17.53% and 59.43%, respectively. The compression response of the radial graded (RG) structure is similar to that of the uniform structure, with minor changes on the mechanical properties and energy absorption capacity. However, the fatigue performance of the RG structure is better than that of the VG structure. With appropriate mechanical properties and changes in pores, this graded structure can simulate the changing physical and chemical properties of natural bone. Therefore, it has great potentiality in the application of bone implants.

Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces

Compared with uniform structures, functionally graded lattice structures can control mechanical properties through varying structures and their volume fraction. In this study, a three-period minimal curved surface method was used to generate functional lattice structure with linear or quadratic function (LF or QF) gradient strategy in the forming direction, and the samples were fabricated by selective laser melting (SLM) using the Ti-6Al-4V metal powder. The mechanical properties, deformation behaviors, and energy absorption performance of graded lattice structures, LF, and QF I-Wrapped Package (IW-P) lattice structures were systematically investigated through experiment and finite element analysis (FEA). Based on the experimental and numerical simulation results, the LF lattice structure shows higher elastic modules and yield strength during small strain period. And the merits of performance increased layer-by-layer under large strain. Additionally, the simulation results based on Johnson-Cook and failure model show that this model can reflect structural compression deformation behavior and mechanical performance prediction. Furthermore, the elastic modulus of LF lattice structure is higher than uniform lattice structures by nearly 61.52% under the same lattice volume fraction. Compared to other lattice structures, the LF or QF lattice structures have better support performance under small strain and stronger energy absorption capacity under large strain with the same volume fraction, respectively, which shows superior potential to be applied to manufacture protective devices or vibration damping devices.

Topology optimization and de-homogenization of graded lattice structures based on asymptotic homogenization

This paper presents a novel two-step homogenization-based topology optimization and de-homogenization method for the design of graded lattice structures. The lattice orientation and material layout are first optimized for square base cells in the macro scale. Then by introducing the lattice stretching design variables of micro base cells, which bridge the base cell distortion with lattice stretch, the error residual of mapping functions is integrated with compliance formulation to form a novel mixed optimization formulation, concurrently optimizing structural performance and mapping functions. The advantage of this formulation is two-fold. First, the micro design space is relaxed from square base cells to rectangular ones so that performance improvement is further expected. Second, an excellent agreement, in both shape and performance, between the projected single-scale lattice structures with the homogenization results is secured, as compared to the frequently adopted post-process procedure of constructing single-scale lattices, where performance deviation could arise for specific microstructural patterns. With the optimized mapping functions, de-homogenization procedure is carried out to construct single-scale spatially graded lattice structures, where a simple filter-projection operation is proposed to obtain fine-scale smoothed boundaries from coarse-scale homogenization results with zig-zag boundaries. Several numerical examples are presented and compared with conventional post-process treatment results to show the validity of the proposed method, and different kinds of lattice patterns adopted in this work show its versatility for a broad range of lattice patterns.

Energy absorption behavior of stiffness optimized graded lattice structures fabricated by material extrusion

Energy absorption behavior of stiffness optimized graded lattice structures fabricated by material extrusion

Crashworthiness improvements of multi-cell thin-walled tubes through lattice structure enhancements

Taking advantage of multi-cell tubes and lattice structures on improving crashworthiness performances, a novel multi-cell thin-walled tube filled with uniform and graded lattice structures is explored in this paper. The body-centered cubic lattice structure is employed as the uniform lattice filler, while the graded lattice filler is constructed by varying the diameter of lattice rods in each layer. Several geometric parameters are investigated numerically, which include the cell number of tube, the dimension of tube and lattice, the height-to-width ratio of the enhanced tube, and the configuration of graded lattices. These parameters are then compared for their crushing load-displacement curves, deformation modes, and energy-absorbing mechanisms. It is observed that the multi-cell tubes exhibit significant improvements to the absorbed energy and crushing force efficiency over the single-cell tubes. In addition, the specific energy absorption (SEA) of the hybrid multi-cell tube structures is improved by 78.6% with respect to the sum of its individual constituents. Furthermore, the multi-cell tube structure filled with graded lattices can present larger energy-absorbing capacity than its uniform lattice counterpart, and the strong end at its top provides better SEA performance. Overall, the hybrid lattice-enhanced tube structure provides an optimal strategy for the crashworthiness design of multi-cell tubes, which can serve as a potential candidate for future crashworthiness applications.

Compressive Properties of Functionally Graded Bionic Bamboo Lattice Structures Fabricated by FDM.

Bionic design is considered a promising approach to improve the performance of lattice structures. In this work, bamboo-inspired cubic and honeycomb lattice structures with graded strut diameters were designed and manufactured by 3D printing. Uniform lattice structures were also designed and fabricated for comparison. Quasi-static compression tests were conducted on lattice structures, and the effects of the unit cell and structure on the mechanical properties, energy absorption and deformation mode were investigated. Results indicated that the new bionic bamboo structure showed similar mechanical properties and energy absorption capacity to the honeycomb structure but performed better than the cubic structure. Compared with the uniform lattice structures, the functionally graded lattice structures showed better performance in terms of initial peak strength, compressive modulus and energy absorption.

Multicomponent topology optimization of functionally graded lattice structures with bulk solid interfaces

AbstractThis article presents a topology optimization method for structures consisting of multiple lattice components under a certain size, which can be manufactured with an additive manufacturing machine with a size limit and assembled via conventional joining processes, such as welding, gluing, riveting, and bolting. The proposed method can simultaneously optimize overall structural topology, partitioning to multiple components and functionally graded lattices within each component. The functionally graded lattice infill with guaranteed connectivity is realized by applying the Helmholtz PDE filter with a variable radius on the density field in the solid isotropic material with penalization (SIMP) method. The partitioning of an overall structure into multiple components is realized by applying the discrete material optimization (DMO) method, in which each material is interpreted as each component, and the size limit for each component imposed by a chosen additive manufacturing machine. A gradient‐free coating filter realizes bulk solid boundaries for each component, which provide continuous mating surfaces between adjacent components to enable the subsequent joining. The structural interfaces between the bulk solid boundaries are extracted and assigned a distinct material property, which model the joints between the adjacent components. Several numeral examples are solved for demonstration.

Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization.

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.